moment.determine

This function reports the largest moment that exists for a collection of
data samples.

We provide two algorithms for monitoring change points with online matrix-valued time series, under the assumption of a two-way factor structure. The algorithms are based on different calculations of the second moment matrices. One is based on stacking the columns of matrix observations, while another is by a more delicate projected approach. A well-known fact is that, in the presence of a change point, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a change point, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a change point. This package also provides some simple functions for detecting and removing outliers, imputing missing entries and testing moments. See more details in He et al. (2021)<arXiv:2112.13479>.

Long Yu

OLCPM

Online Change Point Detection for Matrix-Valued Time Series

Yong He

Xinbing Kong

Lorenzo Trapani

moment.determine function

<dl><dt>x</dt>
<dd>a numeric vector of data samples.</dd>
<dt>k.max</dt>
<dd>a number indicating the upper bound, i.e., at most k.max-th
moment exists.</dd>
<dt>alpha</dt>
<dd>a number in \((0,1)\), indicating the significance level of
the test.</dd>
<dt>R</dt>
<dd>the number of standard Gaussian variables generated in the
randomized test; see also <code>moment.test</code>.</dd></dl>

Arguments

Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu

Author

determine the moment (largest) of the data samples — moment.determine

<dl>

<dt>x</dt>
<dd>a numeric vector of data samples.</dd>


<dt>k.max</dt>
<dd>a number indicating the upper bound, i.e., at most k.max-th
moment exists.</dd>


<dt>alpha</dt>
<dd>a number in \((0,1)\), indicating the significance level of
the test.</dd>


<dt>R</dt>
<dd>the number of standard Gaussian variables generated in the
randomized test; see also <code>moment.test</code>.</dd>

</dl>

moment.determine: determine the moment (largest) of the data samples

Description

Usage

Value

Arguments

Author

Details

Examples